Math problem set Grade 7 Math

Hartsel's Water Rate Increase: A Percent-Change Problem Set

A grade 7 problem set: students compute a town's water bills before and after a rate hike, find percent increases, and check them against affordability guidance.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problems 4, 5, and 6 find the percent increase on a water bill and its base charge, the multistep percent-change work this standard names directly.

All materials for 7.RP.A.3 →

7.EE.B.3 Common Core Math

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, and assess the reasonableness of answers using mental computation and estimation strategies.

How this material aligns: Problems 1, 2, and 8 combine a fixed charge, a decimal per-thousand-gallon rate, and usage into one total bill, the multistep rational-number work this standard requires.

All materials for 7.EE.B.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will compute a monthly water bill from a fixed charge and a volume rate.
Students will find the percent increase between an old and a new bill.
Students will compare a bill to an affordability threshold.

Vocabulary

Key words: base charge, volume rate, percent increase, affordability

Teacher overview

Water utilities raise rates to pay for repairs, and across the country combined water and sewer bills rose about 24 percent from 2019 to 2024. This set follows the fictional town of Hartsel, which is raising rates to replace aging pipes. Students compute a household's bill before and after the change, then find the percent increase and check the new bill against an affordability guideline. A common misconception this set corrects is that the percent increase in the total bill equals the percent increase in the base charge; because usage is charged separately, the two percents are different, as problems 4 and 5 show.

Hartsel's Water Rate Increase: A Percent-Change Problem Set — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

Suppose Hartsel Municipal Water (a fictional utility) uses this billing plan. Imagine the Alvarez household, which uses 6,000 gallons per month.

Current plan: a base charge of $18.00 per month, plus $4.00 for every 1,000 gallons used.
Proposed plan: a base charge of $22.50 per month, plus $4.60 for every 1,000 gallons used.

Find the Alvarez household's current monthly bill at 6,000 gallons.
Find the household's monthly bill under the proposed plan at 6,000 gallons.
How many dollars more per month is the proposed bill than the current bill?
Find the percent increase in the total monthly bill, from the current bill to the proposed bill. Round to the nearest tenth of a percent.
Find the percent increase in just the base charge, from $18.00 to $22.50.
Across the country, combined water and sewer bills rose about 24 percent from 2019 to 2024. Is Hartsel's one-time total increase from problem 4 larger or smaller than that five-year national rise?
The Alvarez household income is $2,000 per month. Affordability guidance treats water and sewer costs above 4.5 percent of income as a high burden. What dollar amount is 4.5 percent of their income, and is the proposed $50.10 water bill alone above or below it?
Suppose the household cuts its use to 4,000 gallons under the proposed plan. Find the new bill and how many dollars it saves compared with using 6,000 gallons.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: $42.00.
6,000 gallons is 6 thousand-gallon units. 6 times $4.00 is $24.00 for volume. $18.00 base plus $24.00 equals $42.00.
Answer: $50.10.
6 times $4.60 is $27.60 for volume. $22.50 base plus $27.60 equals $50.10.
Answer: $8.10.
$50.10 minus $42.00 equals $8.10 more per month.
Answer: 19.3 percent.
The increase is $8.10 on a $42.00 bill. 8.10 divided by 42.00 equals 0.1929, which rounds to 19.3 percent.
Answer: 25 percent.
The base rose $4.50, from $18.00 to $22.50. 4.50 divided by 18.00 equals 0.25, or 25 percent.
Answer: Smaller.
Hartsel's total increase is 19.3 percent, which is smaller than the 24 percent national rise from 2019 to 2024.
Answer: $90.00.
4.5 percent of $2,000 is 0.045 times 2,000, which equals $90.00. The proposed $50.10 bill is below $90.00, so the water bill alone is under the high-burden threshold. Because the guidance covers water and sewer together, a full check would also add the household's sewer charge.
Answer: $40.90.
At 4,000 gallons, volume is 4 times $4.60, which is $18.40. $22.50 base plus $18.40 equals $40.90. That is $50.10 minus $40.90, or $9.20 saved.

Differentiation

Support

Give students a two-row table to organize each bill: one row for the base charge and one row for the volume charge, with a total at the bottom. Work problem 1 together before students continue.

Extension

Ask students to find the exact usage, in gallons, at which the proposed plan would produce a monthly bill of sixty dollars, working backward from the base charge and the volume rate.

ELL supports

Pre-teach "base charge," "volume rate," and "percent increase" with a labeled sample bill showing the two parts added together. Provide a sentence frame for problem 6: "Hartsel's increase is ___ percent, which is ___ than the national rise."